diff --git a/compiler/rustc_middle/src/traits/mod.rs b/compiler/rustc_middle/src/traits/mod.rs
index 53bc9eb7e466c..54cd8cc3efe75 100644
--- a/compiler/rustc_middle/src/traits/mod.rs
+++ b/compiler/rustc_middle/src/traits/mod.rs
@@ -12,7 +12,7 @@ use std::borrow::Cow;
 use std::hash::{Hash, Hasher};
 use std::sync::Arc;
 
-use rustc_errors::{Applicability, Diag, EmissionGuarantee};
+use rustc_errors::{Applicability, Diag, EmissionGuarantee, ErrorGuaranteed};
 use rustc_hir as hir;
 use rustc_hir::HirId;
 use rustc_hir::def_id::DefId;
@@ -996,4 +996,7 @@ pub enum CodegenObligationError {
     /// but was included during typeck due to the trivial_bounds feature.
     Unimplemented,
     FulfillmentError,
+    /// The selected impl has unconstrained generic parameters. This will emit an error
+    /// during impl WF checking.
+    UnconstrainedParam(ErrorGuaranteed),
 }
diff --git a/compiler/rustc_traits/src/codegen.rs b/compiler/rustc_traits/src/codegen.rs
index e5276e6d51585..cc329ca33288c 100644
--- a/compiler/rustc_traits/src/codegen.rs
+++ b/compiler/rustc_traits/src/codegen.rs
@@ -80,16 +80,14 @@ pub(crate) fn codegen_select_candidate<'tcx>(
         // but never resolved, causing the return value of a query to contain inference
         // vars. We do not have a concept for this and will in fact ICE in stable hashing
         // of the return value. So bail out instead.
-        match impl_source {
-            ImplSource::UserDefined(impl_) => {
-                tcx.dcx().span_delayed_bug(
-                    tcx.def_span(impl_.impl_def_id),
-                    "this impl has unconstrained generic parameters",
-                );
-            }
+        let guar = match impl_source {
+            ImplSource::UserDefined(impl_) => tcx.dcx().span_delayed_bug(
+                tcx.def_span(impl_.impl_def_id),
+                "this impl has unconstrained generic parameters",
+            ),
             _ => unreachable!(),
-        }
-        return Err(CodegenObligationError::FulfillmentError);
+        };
+        return Err(CodegenObligationError::UnconstrainedParam(guar));
     }
 
     Ok(&*tcx.arena.alloc(impl_source))
diff --git a/compiler/rustc_ty_utils/src/instance.rs b/compiler/rustc_ty_utils/src/instance.rs
index 8c6e3c86bf5c8..d059d6dcd139c 100644
--- a/compiler/rustc_ty_utils/src/instance.rs
+++ b/compiler/rustc_ty_utils/src/instance.rs
@@ -112,6 +112,7 @@ fn resolve_associated_item<'tcx>(
             | CodegenObligationError::Unimplemented
             | CodegenObligationError::FulfillmentError,
         ) => return Ok(None),
+        Err(CodegenObligationError::UnconstrainedParam(guar)) => return Err(guar),
     };
 
     // Now that we know which impl is being used, we can dispatch to
diff --git a/compiler/rustc_ty_utils/src/layout.rs b/compiler/rustc_ty_utils/src/layout.rs
index b6a14d147cad4..c8b3c8a796f3a 100644
--- a/compiler/rustc_ty_utils/src/layout.rs
+++ b/compiler/rustc_ty_utils/src/layout.rs
@@ -147,12 +147,25 @@ fn extract_const_value<'tcx>(
 ) -> Result<ty::Value<'tcx>, &'tcx LayoutError<'tcx>> {
     match ct.kind() {
         ty::ConstKind::Value(cv) => Ok(cv),
-        ty::ConstKind::Param(_) | ty::ConstKind::Expr(_) | ty::ConstKind::Unevaluated(_) => {
+        ty::ConstKind::Param(_) | ty::ConstKind::Expr(_) => {
             if !ct.has_param() {
                 bug!("failed to normalize const, but it is not generic: {ct:?}");
             }
             Err(error(cx, LayoutError::TooGeneric(ty)))
         }
+        ty::ConstKind::Unevaluated(_) => {
+            let err = if ct.has_param() {
+                LayoutError::TooGeneric(ty)
+            } else {
+                // This case is reachable with unsatisfiable predicates and GCE (which will
+                // cause anon consts to inherit the unsatisfiable predicates). For example
+                // if we have an unsatisfiable `u8: Trait` bound, then it's not a compile
+                // error to mention `[u8; <u8 as Trait>::CONST]`, but we can't compute its
+                // layout.
+                LayoutError::Unknown(ty)
+            };
+            Err(error(cx, err))
+        }
         ty::ConstKind::Infer(_)
         | ty::ConstKind::Bound(..)
         | ty::ConstKind::Placeholder(_)
diff --git a/tests/ui/layout/gce-rigid-const-in-array-len.rs b/tests/ui/layout/gce-rigid-const-in-array-len.rs
new file mode 100644
index 0000000000000..8e57907a2c5ec
--- /dev/null
+++ b/tests/ui/layout/gce-rigid-const-in-array-len.rs
@@ -0,0 +1,27 @@
+//! With `feature(generic_const_exprs)`, anon consts (e.g. length in array types) will
+//! inherit their parent's predicates. When combined with `feature(trivial_bounds)`, it
+//! is possible to have an unevaluated constant that is rigid, but not generic.
+//!
+//! This is what happens below: `u8: A` does not hold in the global environment, but
+//! with trivial bounds + GCE it it possible that `<u8 as A>::B` can appear in an array
+//! length without causing a compile error. This constant is *rigid* (i.e. it cannot be
+//! normalized further), but it is *not generic* (i.e. it does not depend on any generic
+//! parameters).
+//!
+//! This test ensures that we do not ICE in layout computation when encountering such a
+//! constant.
+
+#![feature(rustc_attrs)]
+#![feature(generic_const_exprs)] //~ WARNING: the feature `generic_const_exprs` is incomplete
+#![feature(trivial_bounds)]
+
+#![crate_type = "lib"]
+
+trait A {
+    const B: usize;
+}
+
+#[rustc_layout(debug)]
+struct S([u8; <u8 as A>::B]) //~ ERROR: the type `[u8; <u8 as A>::B]` has an unknown layout
+where
+    u8: A;
diff --git a/tests/ui/layout/gce-rigid-const-in-array-len.stderr b/tests/ui/layout/gce-rigid-const-in-array-len.stderr
new file mode 100644
index 0000000000000..6149debdfe88d
--- /dev/null
+++ b/tests/ui/layout/gce-rigid-const-in-array-len.stderr
@@ -0,0 +1,17 @@
+warning: the feature `generic_const_exprs` is incomplete and may not be safe to use and/or cause compiler crashes
+  --> $DIR/gce-rigid-const-in-array-len.rs:15:12
+   |
+LL | #![feature(generic_const_exprs)]
+   |            ^^^^^^^^^^^^^^^^^^^
+   |
+   = note: see issue #76560 <https://github.com/rust-lang/rust/issues/76560> for more information
+   = note: `#[warn(incomplete_features)]` on by default
+
+error: the type `[u8; <u8 as A>::B]` has an unknown layout
+  --> $DIR/gce-rigid-const-in-array-len.rs:25:1
+   |
+LL | struct S([u8; <u8 as A>::B])
+   | ^^^^^^^^
+
+error: aborting due to 1 previous error; 1 warning emitted
+
diff --git a/tests/ui/layout/unconstrained-param-ice-137308.rs b/tests/ui/layout/unconstrained-param-ice-137308.rs
new file mode 100644
index 0000000000000..c9b1e0a4b9ec3
--- /dev/null
+++ b/tests/ui/layout/unconstrained-param-ice-137308.rs
@@ -0,0 +1,18 @@
+//! Regression test for <https://github.com/rust-lang/rust/issues/137308>.
+//!
+//! This used to ICE in layout computation, because `<u8 as A>::B` fails to normalize
+//! due to the unconstrained param on the impl.
+
+#![feature(rustc_attrs)]
+#![crate_type = "lib"]
+
+trait A {
+    const B: usize;
+}
+
+impl<C: ?Sized> A for u8 { //~ ERROR: the type parameter `C` is not constrained
+    const B: usize = 42;
+}
+
+#[rustc_layout(debug)]
+struct S([u8; <u8 as A>::B]); //~ ERROR: the type has an unknown layout
diff --git a/tests/ui/layout/unconstrained-param-ice-137308.stderr b/tests/ui/layout/unconstrained-param-ice-137308.stderr
new file mode 100644
index 0000000000000..615c131eb9045
--- /dev/null
+++ b/tests/ui/layout/unconstrained-param-ice-137308.stderr
@@ -0,0 +1,15 @@
+error[E0207]: the type parameter `C` is not constrained by the impl trait, self type, or predicates
+  --> $DIR/unconstrained-param-ice-137308.rs:13:6
+   |
+LL | impl<C: ?Sized> A for u8 {
+   |      ^ unconstrained type parameter
+
+error: the type has an unknown layout
+  --> $DIR/unconstrained-param-ice-137308.rs:18:1
+   |
+LL | struct S([u8; <u8 as A>::B]);
+   | ^^^^^^^^
+
+error: aborting due to 2 previous errors
+
+For more information about this error, try `rustc --explain E0207`.